A bstract L ∞ algebras describe the underlying algebraic structure of many consistent classical field theories. In this work we analyze Gauged Double Field Theory in generalized flux formalism. The symmetry transformations consist a deformed Lie derivative and double Lorentz transformations. We obtain all non-trivial products closed form considering Kerr-Schild ansatz for frame include linear p...

With the deep study in this work, we introduce concept of filters a bitonic algebra A. We some fundamental structures such determined filters. also focus on features with respect to homomorphisms. help idea upper sets, investigate basic ideas algebra, and state important theorems related them. obtain relations between algebras sets. an equivalent condition notion

Let g be a Lie algebra over a field k of characteristic zero, and a fix positive integer N. The Lie algebra ĝ = g ⊗k k[t]/t N+1 k[t] is called a truncated current Lie algebra. In this paper a highest-weight theory for ĝ is developed when the underlying Lie algebra g possesses a triangular decomposition. The principal result is the reducibility criterion for the Verma modules of ĝ for a wide cla...